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\author{王立庆（2019级数学与应用数学1班）}
\title{应用随机过程(全英语)：授课计划}
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%\date{2020 年 8 月 28 日}

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\section{课程基本信息}
\begin{itemize}
\item  课程名称：应用随机过程(全英语)
\item  课程属性：专业选修
\item 课程所属学院：统计与数学学院
\item 授课教师：王立庆
\item 学分：2
\item 教学班级：2019级数学与应用数学1班（3071）
\item 选用教材：M. A. Pinsky, S. Karlin, An Introduction to Stochastic Modeling, Fourth Edition, 随机模型概论，机械工业出版社，2013年2月影印版。

\item 上课时间地点：周二下午7-8节，六教312.
\item 答疑时间地点：周二下午12:30-2:30, 周二晚上6:30-8:00, 一教206. 
\item 邮箱：liqingwang@lixin.edu.cn.

\end{itemize}


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\section{教学重点及难点概述}
    \begin{itemize}
    \item 重点：随机过程，离散时间马氏链，状态的分类，平稳分布，极限分布，马氏链基本定理，齐次泊松过程，非齐次泊松过程，复合泊松过程，连续时间马氏链，生灭过程，更新过程，更新定理，布朗运动，反射原理。
    \item 难点：有关随机过程的概率计算。
    \end{itemize}
    

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\section{课时安排 }
\begin{itemize}
\item  本课程总课时：30, 上学期已完成：0, 本学期授课时数安排：30（必修课不含考试周时数）
\end{itemize}
\begin{table}[ht!]\centering
\begin{tabular}{ |M{1.5cm}  |M{1.5cm} |M{1.5cm} |M{1.5cm} |M{1.5cm} |M{1.5cm} |} \hline
课内讲授	&		习题课	&	测验课	&	机动	&	合计	&	课外作业	 \\  \hline
16		&			8	&		6	&	0	&	30	&	60		 \\  \hline
\end{tabular}
\end{table}


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\section{英文授课计划}
%\section{授课计划}
\begin{table}[ht!]\centering
\begin{tabular}{|c|c|c|c|c|}  \hline 
Date		&Week 	&Section	&Content										& Arrangement 			\\[5pt]  \hline 
March 9	&1	 & (3.1-3.3) 	&Markov Chains - Concepts and Examples 			& Lecture 1 			\\[5pt]  \hline 
March 16	&2 	& (3.4-3.5) 	&Markov Chains - First Step Analysis, More Examples 	& Lecture 2			\\[5pt]  \hline 
March 23	&3 	& (4.1-4.4) 	&Markov Chains - Long Run Behaviors 				& Lecture 3			\\[5pt]  \hline 
March 30	&4 	&  			&											& Recitation			\\[5pt]  \hline 
April 6	&5 	& 			&											& {\color{red}Midterm 1}	\\ [5pt] \hline 
April 13	&6 	& (5.1-5.2) 	&Poisson Processes - Concept and Examples  			& Lecture 4	 		\\[5pt]  \hline 
April 20	&7 	& (5.3-5.4) 	&Poisson Processes - Associated Distributions   		& Lecture 5	 		\\[5pt]  \hline 
April 27	&8 	& 			&											& Recitation			\\ [5pt] \hline 
May 4 	&9 	& 			&											&  {\color{red}Midterm 2}	\\ [5pt] \hline 
May 11	&10 	& (6.1) 		&Continuous Time Markov Chains - Pure Birth Processes 	& Lecture 6		 	\\ [5pt] \hline 
May 18	&11 	& (7.1-7.2) 	&Renewal Processes - Block Replacement 			& Lecture 7	 		\\ [5pt] \hline 
May 25	&12 	& (8.1-8.2) 	&Brownian Motions -  the Reflection Principle  			& Lecture 8	 		\\ [5pt] \hline 
June 1 	&13 	& 			&											& Recitation			\\ [5pt] \hline 
June 8	&14 	& 			&											& Recitation			\\ [5pt] \hline 
June 15	&15 	& 			&											&  {\color{red}Final Exam}	\\ [5pt] \hline 
%6月15日	&16	& 			&											& 期末考试			\\ [5pt] \hline 
\end{tabular}
\end{table}
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\section{中文授课计划}
\begin{table}[ht!]\centering
\begin{tabular}{|c|c|c|M{7.5cm}|M{4cm}|}  \hline 
日期	&	周& 	章节&	课程主题&	作业或安排 \\[5pt] \hline 
3月9日&	1&	3.1-3.3&	离散时间马氏链的概念，状态空间，一步和多步转移概率矩阵， CK方程，库存模型&	E3.1.2, P3.1.4, E3.2.2, P3.2.4, E3.3.2, P3.3.6.\\[5pt] \hline
3月16日&	2&	3.4-3.5&	马氏链的第一步分析方法，有吸收态的马氏链，迷宫中的老鼠，最大值过程，部分和过程&	E.3.4.1, E3.4.2, P3.4.1, P3.4.5, E3.5.1, P3.5.4.\\[5pt] \hline
3月23日&	3&	4.1-4.4&	正则马氏链，极限分布和平稳分布，状态的分类：不可约性，常返性，周期性，马氏链的基本极限定理&	E4.1.10, P4.1.1, P4.1.5, E4.2.6, E4.3.2, E4.4.2.\\[5pt] \hline
3月30日&	4&	&	&习题与复述	\\[5pt] \hline
4月6日&	5&	&	&{\color{red}测验一}	\\[5pt] \hline
4月13日&	6&	5.1-5.2&	泊松过程的概念，超市的顾客人数，非齐次泊松过程，泊松分布与二项分布，稀有事件律&	E5.1.1, E5.1.7, P5.1.9, E5.2.1, E5.2.3, P5.2.1.\\[5pt] \hline
4月20日&	7&	5.3-5.4&	等待时间与逗留时间，等待时间的条件分布，复合泊松过程，带折扣的总捐款数&	E5.3.1, E5.3.3, E5.3.7, P5.3.1, E5.4.1, E5.4.3.\\[5pt] \hline
4月27日&	8&	&	&习题与复述	\\[5pt] \hline
5月4日&	9&	&	&{\color{red}测验二}	\\[5pt] \hline
5月11日&	10&	6.1&	连续时间马氏链，泊松过程，纯生过程，转移速率，常微分方程，Yule过程&	E6.1.1, E6.1.2, P6.1.1, P6.1.2.\\[5pt] \hline
5月18日&	11&	7.1-7.2&	更新过程，更新函数，Wald等式，更换灯泡的优化策略&	E7.1.2, E7.1.3, E7.2.1, E7.2.3, P7.2.1.\\[5pt] \hline
5月25日&	12&	8.1-8.2&	布朗运动的概念，转移概率密度函数，与随机行走的关系，极大值过程，首中时	&E8.1.1, E8.1.2, E8.1.4, P8.1.1, P8.1.3, E8.2.1.\\[5pt] \hline
6月1日&	13&	&	&习题与复述	\\[5pt] \hline
6月8日&	14&	&	&习题与复述	\\[5pt] \hline
6月15日&	15&	&	&{\color{red}期末考试}	\\[5pt] \hline
\end{tabular}
\end{table}


注：
\begin{itemize}
\item 日期是指每周的星期二。
\item 正文课：老师讲解理论和例子，英语板书，英汉双语讲解。
\item 习题与复述课：学生讲解作业。一共45个课后作业题。
\end{itemize}


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